Create noise texture and set its influence rgb value?
Here's some sample code for creating a new material, texture slot, texture and setting it all up together as specified in your question:

m                   = bpy.data.materials.new( "MyMat" )
m.diffuse_color     = (1, 1, 1);
obj.active_material = m

ts                      = m.texture_slots.create(0)
ts.texture_coords       = 'UV' # Assuming this is what you want, could be any of the following: ('GLOBAL', 'OBJECT', 'ORCO', 'UV', 'STRAND', 'WINDOW', 'NORMAL', 'REFLECTION', 'STRESS', 'TANGENT')
ts.color                = (0.45778, 1, 0.223341)
ts.texture              = bpy.data.textures.new( "TEXTURE", "NOISE" )